Question

Prove that, sin²32 + sin² 58 - tan² 45 = 0.​

Answer 1

Step-by-step explanation:

kindly refer the above attachment hope you understand the answer

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Answer 2

$\huge\bf\underline{\underline{To\: Prove:}}$

$sin^{2} 32 + sin^{2} 58 - tan^{2} 45 =0$

$\huge\bf\underline{\underline{Proof:}}$

LHS:

$sin^{2} 32 + sin^{2} 58 - tan^{2} 45 \\ { \sin }^{2} 32 + cos ^{2}(90 - 58) - {tan}^{2} 45 \\ {sin}^{2} 32 + {cos}^{2} 32 - </strong><strong>(</strong><strong>1</strong><strong>)</strong><strong> </strong><strong>^</strong><strong>2</strong><strong>\\ 1 - 1 \\ 0</strong><strong>=</strong><strong>RHS\</strong><strong>\</strong><strong>H</strong><strong>e</strong><strong>n</strong><strong>c</strong><strong>e</strong><strong> </strong><strong>Proved</strong><strong>$

Formulas Used:

$sin \theta = cos(90 - \theta) \\ {sin}^{2} \theta + cos^{2} \theta = 1$

Trigonometric Values Used:

$\tan(45) = 1$

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